Absolute lost at words for how to describe this softbody/fluid?
This is a soft body plastic deformation and tearing simulation. Currently, Blender's built-in soft body system does not support tearing, and (to my knowledge) the Mantaflow fluid system is not appropriate for the extremely high viscosities needed to emulate it.
Thankfully, there are a couple of free options you can use:
Molecular Addon
Probably your best bet, the Molecular addon uses a very flexible meshless mass-spring system to approximate a wide range of soft body physics (when combined with CubeSurfer) as well as simulate granular flow. Most relevant to your problem is the feature for breaking bonds. Unfortunately the documentation is offline, so I cannot link it to you now.
FLIP Fluids
FLIP Fluids is a fluid solver for blender that supports high-viscosity liquids. While it appears to be a paid addon, it is possible to use it if you compile from source. For your problem, all you need to do is crank the fluid viscosity up and have a blob of fluid in the initial shape of your body.
In the future, I hope the new soft body sim and particle nodes will be up to the task.